Algorithm to locate points in a Delaunay triangulation

We present an algorithm to locate quickly the positions of several points within triangles of a given Delaumay triangulation in the plane. The proposed algorithm locates the query point simply by determining the closest node in the triangulation then by testing elements connected to that node within a small often pre-computable Graph-Theoretic Radius (GTR). A bound on the graph-theoretic radius containing the query point is derived and its relation is characterized analytically in terms of the sharpness of the elements angles. Empirical results show that this procedure is more efficient in practice than existing algorithms.